I ran a few test with Lurker/Graverobber in the Kingdom. I have only seen it get stuck after playing Lurker when there is a card in the trash it can gain. I have managed to get it to play Lurker when there is nothing it can gain in which case it doesn't trash anything and just continues on with its turn.

I have seen it play Graverobber and continue on with its turn normally, I assume this only happens when it cannot trash anything and it cannot gain a card from the trash. It seems to get stuck when it can trash and/or gain a card.

I also decided to see what happens when there are two cards in the trash that it could gain with a Rouge. It gained a card without getting stuck.

This suggest that it is something about the choice of being able to trash a card or gain a card from the trash that causes it to get stuck in an infinite loop. I hope this helps to fix the problem.

Your Lurker experience is the same same as mine: When the game can continue legally with "no action taken", that will happen with Lurker. Usually that means that there is no action card in the trash, because in 99.9% of cases there still are action cards in the supply.

You wrote "...that it could gain with a Rouge" (emphasis mine). Did you really test with Rogue, or did you mistype and you tested with Graverobber?

I meant Rouge. I decided to test with Rouge because it is able to gain a card from the trash just like Lurker and Graverobber can, the only difference between Rouge and Graverobber/Lurker is that Rouge forces you to gain from the trash if there is a card in there that you can gain where as with Graverobber/Lurker you always have that choice to gain or trash, so I wanted to see if it was the ability to gain a card from the trash that was messing with the AI or if it was something unique to Graverobber/Lurker.

With my Rouge test I had a Rouge and a Gold in the trash and managed to get the AI to play a Rouge. It was able to gain the Gold from the trash without problem even though there were two cards (not an automatic gain) suggesting that it does have the ability to pick a card from the trash, so it appears that the bug has something to do with Lurker's/Graverobber's choose one ability.